# Load Test Question

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#### proppastie

##### Well-Known Member
Log Member
See if you can fix it
Here is my working spread sheet with the examples I used to do the calculation....I really need worked examples.....not as smart as some people

see post 86 for revised xls

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#### tdfsks

##### Well-Known Member
Example follows:

Note: this approximate method only works for a thin web with relatively heavy caps. Use it on a rectangular spruce spar and it will under predict the shear stress by 50% !!! It is important to understand the theory ...

This calculation is pretty close for your load test because you hung the loading close to the spar web and there was minimal torsion. For more realistic loading case there will be more torsion load and the method in my previous post is required.

#### wsimpso1

##### Super Moderator
Staff member
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The added angle shown above, will increase bending stiffness about 17%. Trouble is that this new angle's flange has the same susceptibility to compression driven buckling as the original. It will decrease compression loads in those angles 17%, which will raise the bending moment before you get to critical load, but I suspect will not be enough. We may need substantially larger resistance to buckling.

You could brute force the design by making the new angles thicker until you can get buckling beyond target g's. Since the original angle is still in there, this option may be no worse than others.

Earlier I suggested putting a return flange on the added angle (now a channel) , while Proppastie suggested a z section. Exploring shapes other than a simple angle that have higher critical stresses for buckling as well as raising total section stiffness could allow you to get to strength at lower added weight.

While adding a second angle to each cap/skin is more efficient, bend radii limits as you add thickness to the shape may restrict how much you can add. Perhaps adding lamina to the cap will get you there too.

This also suggests that for demonstrating enough improvement you could add and/or change shapes riveted to the existing caps and angles, but for final design, you might simply make the angle into a single thicker angle or other shape. The counterpoint would be that the added pieces may only be needed near the root, making even bulky add-ons still pretty light.

Billski

#### tdfsks

##### Well-Known Member
Yes I agree ... the figure above was just meant to understand whether an extra angle can be added considering rivet placement etc. Now that we have confirmed that the spar cap is on the front of the spar at the root and there is plenty of space, we will need to look at the design of that reinforcing angle. I agree that it will have a return on the free edge to help raise the buckling stress. Unfortunately it will need to be in segments between the ribs in the first few bays.

I have some concerns about the buckling of the spar and the web as well and are still looking at that before I post any calcs. The spar buckling is difficult to predict analytically because of the way that it is stabilized by the angle stiffeners. From the calculations I have done so far, I would say that the spar web will definitely buckle at higher loads but that is the case with most shear webs in metal wings. We will need to make some judgement as to whether we are willing to accept the buckling once we fully understand when and how it will occur.

#### BBerson

##### Light Plane Philosopher
HBA Supporter
I built and tested a wing D-cell almost like this. The caps were stacked (laminated) .032" 2024-t3 formed angles.
The laminated angles didn't work as expected and started to buckle in compression between the rivets. I added an additional angle of .125" extrusion. The lesson was that laminations are not the same as a solid bar or a thick angle in compression.

#### proppastie

##### Well-Known Member
Log Member
Fixed it, (I think)...subtracted area to the rivet line....using revised section properties and following your example. thank you.

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#### tdfsks

##### Well-Known Member
I built and tested a wing D-cell almost like this. The caps were stacked (laminated) .032" 2024-t3 formed angles.
The laminated angles didn't work as expected and started to buckle in compression between the rivets. I added an additional angle of .125" extrusion. The lesson was that laminations are not the same as a solid bar or a thick angle in compression.
Yes, in a stack like this, it is normal practice to check the crippling stress for each element separately. They do not behave as one homogeneous angle of X number of lamination's in thickness.

We also need to be mindful of interrivet buckling where thin web or skin can buckle as a column between rivets where the web or skin is riveted to a spar cap or similar.

This is tricky stuff and these local failure modes highlight why FEA analysis is pretty useless in cases like this, unless you just use it to extract the net section stresses and then go and check all these failure modes manually.

#### tdfsks

##### Well-Known Member
What is the size and thickness of the web stiffener angles. What is their spacing on the web ?

#### proppastie

##### Well-Known Member
Log Member
.5x.5 angle 2024-T3 stiffeners
.025, 2 inch spacing until WS 51,
.016 2.3 inch spacing to.ws 93.75,
2.4 spacing to ws157.875,
3 inch spacing to ws 179.25,
3.8 spacing to ws 200.63,
5.3 spacing to ws 222
no more stiffeners after ws 222

Cap thickness same top and bottom with over laps for bolted splice for example at ws 48 there would be 5/8 thickness for 2.562 span overlap inboard from WS 48 ( the cap-strips were max 48" long)
1/4 to ws 93.75
3/16 to ws 136.5
1/8 to ws 179.25
1/16 to ws 243.38

EDIT.....5/16 cap to ws 72.375

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#### tdfsks

##### Well-Known Member
OK .... here is the first installment of the buckling calculations for the spar root area. There will be a few steps after this to build up the complete picture of what is going on.

First here are the spar dimensions that I am working with:

Today's step is to check the inter-rivet buckling to verify that rivet spacing is close enough. If rivets are too far apart the sheet being secured will buckle as small columns between the rivets, limiting the amount of load that can be carried.

Check Inter-rivet Buckling of Web:

The web is secured to the caps with MS20470AD3 rivets spaced at 3/4". The web is 0.025" thick. This is a check to see whether the edge of the web will remain flat or bulge (buckle) between rivets.

I do these calculations in a spreadsheet but you can see the graphs and equations used and easily follow along with a calculator. These calculations are straight from Bruhn "Analysis and Design of Aerospace Structures" 1973. Note that there are two separate methods used. The first method relies on the graph and is straight forward. The second method uses an equation and one of the inputs is the tangent modulus (Et). I have not shown where the tangent modulus came from but I got it from MIL-HDBK-5F for 2024-T3 sheet. I suggest just using the first method with the graph. The second method is only really required when countersunk rivets are used.

The inter rivet buckling stress (Fir) is approx 28 ksi.

From previous calculations, the bending stress at limit load is approx 16.1 ksi limit (24.1 ksi ultimate) at the edge of the web with the full section unbuckled and effective.

Since the bending stress at ultimate load is 24.1 ksi, which is less than the buckling stress, the web will not buckle at ultimate loads. So far so good ....

Check Inter-Rivet Buckling of Skin:

The skin is 0.016" and is riveted to the top and bottom of the spar. Rivet spacing is 1".

OK ... so the inter-rivet buckling stress (Fir) of the skin is 9 ksi.

From previous calculations, the bending stress in the skin was 16.5 ksi (limit) or 24.7 ksi (ultimate)

Clearly the skin will buckle between rivets before the limit load is reached ... in fact we were not far short of that occurring at the point the load test was terminated (6 ksi from memory).

Decision time. Do we let it buckle and just remove the contribution of the effective width of skin from our bending stress calculations or do we halve the rivet pitch for a higher buckling stress ?

Lets see what happens when the rivet pitch is halved .....

With half the rivet pitch (0.5") the buckling stress (Fir) jumps to 27.5 ksi which is above the ultimate bending stress (24.7 ksi). A worthwhile improvement but a lot of extra rivets to add.

The effective width of the skin is quite small and its contribution to bending would not be that great. I think this is an optional improvement ..... unless the buckling becomes significant and starts popping heads off rivets in the test. These are only 3/32" dia rivets after all. Time will tell.

Tomorrow more checks of different buckling modes.

#### plncraze

##### Well-Known Member
HBA Supporter
Good stuff! Thanks and keep it coming!

#### proppastie

##### Well-Known Member
Log Member
A worthwhile improvement but a lot of extra rivets to add.
No need to comment at this time but something to think about.
That flange is easy to get to and easy to rivet......adding a rivet line and Z stiffener between the rivet line and spar is possible.

Also thinking about the worse bending at the outboard attach of the drag spar.......there was a slight incline forward of the setup, so bending of the spar in the airplane forward X direction was a possibility.....thinking about possible addition of more bracing.....see photos.

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#### tdfsks

##### Well-Known Member
I think the next step is to check the buckling of the shear web.

So far we have calculated the following stresses in the web:
Shear Stress = 2725 psi (limit) and 4088 psi (ultimate)
Bending Stress at top and bottom edge of the web = 16094 psi (Limit) and 24141 psi (ultimate)

To begin I will reproduce the figure from yesterdays post that provides all the dimensions of the web at the wing root.

The web is 10.5" deep and 0.025" thick.

Initially ignore the stiffeners and assume that the web is unstiffened between the ribs as an example to show the effect of stiffening. So the length is initially 21 in long.

Calculate Buckling Stress Due to Web Shear (No Stiffeners):

The calculations are done in a spreadsheet but this formatted similarly to a hand written calculation and it is easily followed.
The edges of the web secured by rivets have been assumed to have edge fixity mid way between a hinged and clamped edge.

Note that the shear stress in the web (2725 psi limit and 4088 psi) is substantially higher than the buckling stress 460.5 psi. This buckling stress does not mean that the web fails at this stress but it buckles out of plane and there is a loss of stiffness and its ability to carry higher loads is reduced. A tension field would form in the web if loading progressed to higher loads (i.e. the web would start to develop wrinkles at 45 deg).

Note also that the wave length of the buckles is 13.125".

Calculate Buckling Stress Due to Web Bending:

Clearly the buckling stress (2357.4 psi) is much lower than the applied bending stress of 16094 psi (limit) and 24141 psi (ultimate).
The wave length of the buckling is 7 inches.

Use of Stiffeners:

Given the wave length of the shear and bending buckling, 13.125" and 7" respectively, closely spaced stiffeners can be added to help control the buckling and hold the web in a planar position to increase the buckling stresses. In this case vertical stiffeners have been added in the root area at 2" spacing. The stiffeners are 0.5" x 0.5" x 0.025" angles.

Repeat Shear Buckling Calculations For Small Panels:
With stiffeners installed, the shear web is now divided into smaller panels 2" wide and 10.5" high.
The shear buckling calculations are repeated for these smaller panels.

Note that the critical buckling stress in shear is now 11332 psi which is substantially higher than the applied applied shear stresses of (2725 psi limit and 4088 psi). So the stiffeners have prevented shear buckling.

Repeat Bending Buckling Calculations For Small Panels:

There is no improvement in the buckling stress due to the addition of the stiffeners. So the additional of the stiffeners will not prevent the web from buckling due to the bending stresses. The stiffeners will control the magnitude of the buckles and enforce a shorter wavelength but do not eliminate the web buckling. Again this does not mean that the spar web will fail - it can continue to sustain higher loads once the initial buckling stress has been passed but additional bending load added after buckling will need to be carried by the caps.

If longitudinal stiffeners are added to further divide the web into smaller panels, higher stresses can be achieved prior to the web buckling.

Consider adding 2 x longitudinal stiffeners equally spaced between the caps to divide the 10.5" web dimension into 3 spaces (i.e. 10.5/3 = 3.5). The resulting shear panels are now 2" x 3.5".

The buckling stress has now increased to 21215 psi. So the web would now remain unbuckled to a point approx midway between limit load (16094 psi) and the ultimate load (24141 psi). A decision will need to be made on whether to add these stiffeners or just let the web buckle. This decision might be influenced by further load testing during which the web buckling can be monitored. Remember that it has been verified by previous calculations that the edges of of the shear web is adequately secured by the rivets to prevent inter rivet buckling. So the web buckling due to bending will be characterized by buckles inboard of the caps between the stiffeners.

Web Stiffener Sizing:
Check the size of the web stiffeners to ensure that they have sufficient stiffness to control web buckling:

The size of the web stiffeners is more than adequate.
Rivet spacing does not comply with the suggested spacing. Again the effects of this can be monitored in future load testing.

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#### proppastie

##### Well-Known Member
Log Member
I am not sure how I can possibly thank you for your work....With these real-world calculations/examples perhaps I can go further with analysis at different wing stations along the spar and effect a reasonable fix.......Please continue if you so desire I certainly can use all the help I can get.

I need to study this before I feel I can ask any intelligent questions.

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#### plncraze

##### Well-Known Member
HBA Supporter
Thank for including edge fixity. That is something I have read but not seen in practice. Can't thank you enough for sharing this stuff.

#### proppastie

##### Well-Known Member
Log Member
Again this does not mean that the spar web will fail - it can continue to sustain higher loads once the initial buckling stress has been passed but additional bending load added after buckling will need to be carried by the caps.
If the Caps are able to carry the bending load, will the web still wrinkle/collapse?, and what about the stiffeners? If they do not fail/buckle how does the web and spar fail? What might it look like?

#### tdfsks

##### Well-Known Member
Based on the calculations to date, I don't think the web is likely to collapse. There will likely be some wrinkling as the load is increased. This is normal in sheet metal wings.

The idea of doing calculations for the buckling is that it gives us a good idea of where to expect problems and we can monitor those failure modes during loading.

The stresses in the spar caps are relatively low. My main concern is the buckling of the spar cap and unfortunately this would be a failure that could occur suddenly with little warning. The buckling is not that easy to analyse. As a pure column between ribs, with web stiffeners, the inner edge of the compression cap would become unstable and buckle out of the plane of the web. The outboard edge would be restrained by the web connection to the leading edge and the flange on the web (assuming we beef that up to stop it buckling first). However, when you add the web stiffeners, they effectively stabilize the cap and help prevent it rotating out of plane and so raise the buckling stress.

We also need to resolve the issues with the leading edge skin. I have some thoughts on this but I need to do some more work on this before I am ready to discuss it.

The first goal should be to get the wing to pass the load test you have set up. The next step would be to put it at an angle of attack and repeat the test to verify the strength of the drag bracing and I can see a few more issues there ... anyway one step at a time.

I am going to be away for the next week and will not be able to do any calculations whilst I am away. We can pick that up in a week ... however we can continue to discuss this issues whilst I am travelling.

#### BBerson

##### Light Plane Philosopher
HBA Supporter
What part of the D-cell skin is buckling? I can't really see it in the photo.

#### plncraze

##### Well-Known Member
HBA Supporter
In the very first post it is the second from last picture. It's looks like the diagonal piece of the rib is pulling down the skin.

#### plncraze

##### Well-Known Member
HBA Supporter
TDFSKS said this rib usually has a way to put the load somewhere else but this inner rib does not attach to anything else. On some airplanes you have a little bracket from the front f this rib that allows the leading edge loads to be carried into the fuselage under high positive angle of attack operation.